Anyone who might have thought Everton would have Tuesday’s big FA Cup tie at Sunderland on their minds clearly doesn’t know David Moyes.

The Toffees manager does ­nothing by half-measures. He sent out a side at the ­Liberty Stadium to strangle the life out of Swansea City and soften them up for two ­second-half dagger thrusts.

It was a result that will act as a timely warning to the Swans that, despite their ­remarkable success in their first season in the Premier League, their pleasing ­passing style won’t work against all of their ­opponents.

Especially when they are as committed, organised, ­efficient and as ruthless as Everton were yesterday.

Moyes said: “This was a big win for us today. I haven’t even thought about the FA Cup replay until now.

“I felt we ­deserved the win. We stopped Swansea from displaying that passing fluency that has been a feature of their game.

“And the goal from Leighton Baines was exquisite – he’s got a wonderful left foot in situations like that.”

Swansea manager Brendan Rodgers said: “All credit to Everton, they came and earned their win.

“We weren’t quite at our best today – and that’s what happens at this level.

“This is the toughest league in the world. If you dip just a little the other team will take full advantage”

Moyes had done his ­homework on Swansea, ­seeking to throttle their midfield engine-room of Leon Britton, Joe Allen and Gylfi Sigurdsson by man-marking them and making it difficult for the Swans to operate with their usual fluency.

There were a few moments of alarm in Everton’s danger area when Danny Graham fired tamely at Tim Howard and Wayne Routledge blasted a close-range drive high over the crossbar.

But it was a first half of hard labour for the Welsh side. And Everton, having established a real foothold, began to show more adventure before the interval.

Swansea survived the pressure with no real concern. But there was still enough frustration for Allen to be booked for a high challenge on Phil Neville seconds before the break.

Everton began the second half with some real attacking vigour. It needed a stunning save by Michel Vorm, who flung himself across his line to beat out Darren Gibson’s 25-yard blockbuster.

But even Vorm – so often Swansea’s saviour this season – was powerless to stop Baines firing Everton ahead after 59 minutes. Free-kicks have ­become the trademark of the England full-back and he ­provided one of those special strikes again.

His left-foot shot from just outside the area curled ­perfectly into the corner of the net after he himself had been fouled by Ashley Williams.

Swansea continued to toil but still Everton dominated and Nikica Jelavic drilled home their second on 76 ­minutes after Marouane Fellaini had set up the opening.